MP Board Class 12th Maths Solutions Guide pdf free download गणित हिंदी मीडियम छात्रों के लिए MP Board Class 12th Solutions का यह हिस्सा 12वीं मैथ के विद्यार्थियों के लिए अति महत्वपूर्ण हैं। यहां हमने NCERT Madhya Pradesh Syllabus MP Board Class 12 Maths Book Solution Ganit Pdf दिया है।
छात्र को बता दें कि सभी छात्र पूरे पाठ्यक्रम को पढ़ने और समझने के बाद अपनी परीक्षाओं में अधिक से अधिक अंक प्राप्त करने करने के लिए Mp board 12th model paper भी डाउनलोड कर सकते हैं।NCERT MP Board Class 12th Maths Book Solutions in Hindi Medium
MP Board Class 12th Maths Chapter 1 Relationship and function (संबंध एवं फलन)
- 12th Chapter 1 Relationship and function Ex 1.1
- 12th Chapter 1 Relationship and function Ex 1.2
- 12th Chapter 1 Relationship and function Ex 1.3
- 12th Chapter 1 Relationship and function Ex 1.4
- 12th Chapter 1 Relationship and function Ex विविध प्रश्नावली
MP Board Class 12th Maths Chapter 2 प्रतिलोम त्रिकोणमितीय फलन
- Chapter 2 प्रतिलोम त्रिकोणमितीय फलन Ex 2.1
- Chapter 2 प्रतिलोम त्रिकोणमितीय फलन Ex 2.2
- Chapter 2 प्रतिलोम त्रिकोणमितीय फलन विविध प्रश्नावली
MP Board Class 12th Maths Chapter 3 आव्यूह
- Chapter 3 आव्यूह Ex 3.1
- Chapter 3 आव्यूह Ex 3.2
- Chapter 3 आव्यूह Ex 3.3
- Chapter 3 आव्यूह Ex 3.4
- Chapter 3 आव्यूह विविध प्रश्नावली
MP Board Class 12th Maths Chapter 4 सारणिक
- Chapter 4 सारणिक Ex 4.1
- Chapter 4 सारणिक Ex 4.2
- Chapter 4 सारणिक Ex 4.3
- Chapter 4 सारणिक Ex 4.4
- Chapter 4 सारणिक Ex 4.5
- Chapter 4 सारणिक Ex 4.6
- Chapter 4 सारणिक विविध प्रश्नावली
MP Board Class 12th Maths Chapter 5 सांतत्य तथा अवकलनीयता
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.1
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.2
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.3
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.4
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.5
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.6
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.7
- Chapter 5 सांतत्य तथा अवकलनीयता Ex 5.8
- Chapter 5 सांतत्य तथा अवकलनीयता विविध प्रश्नावली
MP Board Class 12th Maths Chapter 6 अवकलज के अनुप्रयोग
- Chapter 6 अवकलज के अनुप्रयोग Ex 6.1
- Chapter 6 अवकलज के अनुप्रयोग Ex 6.2
- Chapter 6 अवकलज के अनुप्रयोग Ex 6.3
- Chapter 6 अवकलज के अनुप्रयोग Ex 6.4
- Chapter 6 अवकलज के अनुप्रयोग Ex 6.5
- Chapter 6 अवकलज के अनुप्रयोग विविध प्रश्नावली
MP Board Class 12th Maths Chapter 7 समाकलन
- Chapter 7 समाकलन Ex 7.1
- Chapter 7 समाकलन Ex 7.2
- Chapter 7 समाकलन Ex 7.3
- Chapter 7 समाकलन Ex 7.4
- Chapter 7 समाकलन Ex 7.5
- Chapter 7 समाकलन Ex 7.6
- Chapter 7 समाकलन Ex 7.7
- Chapter 7 समाकलन Ex 7.8
- Chapter 7 समाकलन Ex 7.9
- Chapter 7 समाकलन Ex 7.10
- Chapter 7 समाकलन Ex 7.11
- Chapter 7 समाकलन विविध प्रश्नावली
MP Board Class 12th Maths Chapter 8 समाकलनों के अनुप्रयोग
- Chapter 8 समाकलनों के अनुप्रयोग Ex 8.1
- Chapter 8 समाकलनों के अनुप्रयोग Ex 8.2
- Chapter 8 समाकलनों के अनुप्रयोग विविध प्रश्नावली
MP Board Class 12th Maths Chapter 9 अवकल समीकरण
- Chapter 9 अवकल समीकरण Ex 9.1
- Chapter 9 अवकल समीकरण Ex 9.2
- Chapter 9 अवकल समीकरण Ex 9.3
- Chapter 9 अवकल समीकरण Ex 9.4
- Chapter 9 अवकल समीकरण Ex 9.5
- Chapter 9 अवकल समीकरण Ex 9.6
- Chapter 9 अवकल समीकरण विविध प्रश्नावली
MP Board Class 12th Maths Chapter 10 सदिश बीजगणित
- Chapter 10 सदिश बीजगणित Ex 10.1
- Chapter 10 सदिश बीजगणित Ex 10.2
- Chapter 10 सदिश बीजगणित Ex 10.3
- Chapter 10 सदिश बीजगणित Ex 10.4
- Chapter 10 सदिश बीजगणित विविध प्रश्नावली
MP Board Class 12th Maths Chapter 11 त्रि-विमीय ज्यामिति
- Chapter 11 त्रिविमीय ज्यामिति Ex 11.1
- Chapter 11 त्रिविमीय ज्यामिति Ex 11.2
- Chapter 11 त्रिविमीय ज्यामिति Ex 11.3
- Chapter 11 त्रिविमीय ज्यामिति विविध प्रश्नावली
MP Board Class 12th Maths Chapter 12 रैखिक प्रोग्रामन
- Chapter 12 रैखिक प्रोग्रामन Ex 12.1
- Chapter 12 रैखिक प्रोग्रामन Ex 12.2
- Chapter 12 रैखिक प्रोग्रामन विविध प्रश्नावली
MP Board Class 12th Maths Chapter 13 प्रायिकता
- Chapter 13 प्रायिकता Ex 13.1
- Chapter 13 प्रायिकता Ex 13.2
- Chapter 13 प्रायिकता Ex 13.3
- Chapter 13 प्रायिकता Ex 13.4
- Chapter 13 प्रायिकता Ex 13.5
- Chapter 13 प्रायिकता विविध प्रश्नावली
MP Board Class 12th Maths Book Solutions in English Medium
MP Board Class 12th Maths Chapter 1 Relations and Functions
- Chapter 1 Relations and Functions Ex 1.1
- Chapter 1 Relations and Functions Ex 1.2
- Chapter 1 Relations and Functions Ex 1.3
- Chapter 1 Relations and Functions Ex 1.4
- Chapter 1 Relations and Functions Miscellaneous Exercise
MP Board Class 12th Maths Chapter 2 Inverse Trigonometric Functions
- Chapter 2 Inverse Trigonometric Functions Ex 2.1
- Chapter 2 Inverse Trigonometric Functions Ex 2.2
- Chapter 2 Inverse Trigonometric Functions Miscellaneous Exercise
MP Board Class 12th Maths Chapter 3 Matrices
- Chapter 3 Matrices Ex 3.1
- Chapter 3 Matrices Ex 3.2
- Chapter 3 Matrices Ex 3.3
- Chapter 3 Matrices Ex 3.4
- Chapter 3 Matrices Miscellaneous Exercise
MP Board Class 12th Maths Chapter 4 Determinants
- Chapter 4 Determinants Ex 4.1
- Chapter 4 Determinants Ex 4.2
- Chapter 4 Determinants Ex 4.3
- Chapter 4 Determinants Ex 4.4
- Chapter 4 Determinants Ex 4.5
- Chapter 4 Determinants Ex 4.6
- Chapter 4 Determinants Miscellaneous Exercise
MP Board Class 12th Maths Chapter 5 Continuity and Differentiability
- Chapter 5 Continuity and Differentiability Ex 5.1
- Chapter 5 Continuity and Differentiability Ex 5.2
- Chapter 5 Continuity and Differentiability Ex 5.3
- Chapter 5 Continuity and Differentiability Ex 5.4
- Chapter 5 Continuity and Differentiability Ex 5.5
- Chapter 5 Continuity and Differentiability Ex 5.6
- Chapter 5 Continuity and Differentiability Ex 5.7
- Chapter 5 Continuity and Differentiability Ex 5.8
- Chapter 5 Continuity and Differentiability Miscellaneous Exercise
MP Board Class 12th Maths Chapter 6 Application of Derivatives
- Chapter 6 Application of Derivatives Ex 6.1
- Chapter 6 Application of Derivatives Ex 6.2
- Chapter 6 Application of Derivatives Ex 6.3
- Chapter 6 Application of Derivatives Ex 6.4
- Chapter 6 Application of Derivatives Ex 6.5
- Chapter 6 Application of Derivatives Miscellaneous Exercise
MP Board Class 12th Maths Chapter 7 Integrals
- Chapter 7 Integrals Ex 7.1
- Chapter 7 Integrals Ex 7.2
- Chapter 7 Integrals Ex 7.3
- Chapter 7 Integrals Ex 7.4
- Chapter 7 Integrals Ex 7.5
- Chapter 7 Integrals Ex 7.6
- Chapter 7 Integrals Ex 7.7
- Chapter 7 Integrals Ex 7.8
- Chapter 7 Integrals Ex 7.9
- Chapter 7 Integrals Ex 7.10
- Chapter 7 Integrals Ex 7.11
- Chapter 7 Integrals Miscellaneous Exercise
MP Board Class 12th Maths Chapter 8 Application of Integrals
- Chapter 8 Application of Integrals Ex 8.1
- Chapter 8 Application of Integrals Ex 8.2
- Chapter 8 Application of Integrals Miscellaneous Exercise
MP Board Class 12th Maths Chapter 9 Differential Equations
- Chapter 9 Differential Equations Ex 9.1
- Chapter 9 Differential Equations Ex 9.2
- Chapter 9 Differential Equations Ex 9.3
- Chapter 9 Differential Equations Ex 9.4
- Chapter 9 Differential Equations Ex 9.5
- Chapter 9 Differential Equations Ex 9.6
- Chapter 9 Differential Equations Miscellaneous Exercise
MP Board Class 12th Maths Chapter 10 Vector Algebra
- Chapter 10 Vector Algebra Ex 10.1
- Chapter 10 Vector Algebra Ex 10.2
- Chapter 10 Vector Algebra Ex 10.3
- Chapter 10 Vector Algebra Ex 10.4
- Chapter 10 Vector Algebra Miscellaneous Exercise
MP Board Class 12th Maths Chapter 11 Three Dimensional Geometry
- Chapter 11 Three Dimensional Geometry Ex 11.1
- Chapter 11 Three Dimensional Geometry Ex 11.2
- Chapter 11 Three Dimensional Geometry Ex 11.3
- Chapter 11 Three Dimensional Geometry Miscellaneous Exercise
MP Board Class 12th Maths Chapter 12 Linear Programming
- Chapter 12 Linear Programming Ex 12.1
- Chapter 12 Linear Programming Ex 12.2
- Chapter 12 Linear Programming Miscellaneous Exercise
MP Board Class 12th Maths Chapter 13 Probability
- Chapter 13 Probability Ex 13.1
- Chapter 13 Probability Ex 13.2
- Chapter 13 Probability Ex 13.3
- Chapter 13 Probability Ex 13.4
- Chapter 13 Probability Ex 13.5
- Chapter 13 Probability Miscellaneous Exercise
MP Board Class 12th Maths Syllabus and Marking Scheme
Latest Syllabus and Marks Distribution Maths Class XII for the academic year 2019 – 2020 Year Examination.
Maths
Class XII
Time : 3 Hours.
Maximum Marks: 100
Unit Wise Division of Marks
Unit | Topics | Periods | Marks |
I. | Relations and Functions | 30 | 10 |
II. | Algebra | 50 | 13 |
III. | Calculus | 80 | 44 |
IV. | Vectors and Three-dimensional Geometry | 30 | 17 |
V. | Linear Programming | 20 | 06 |
VI. | Probability ‘ | 30 | 10 |
Total | 240 | 100 |
Unit I: Relations and Functions
1. Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence
relations. One to one and onto functions, composite functions, inverse
of a function. Binary operations.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse
trigonometric functions. Elementary properties of inverse trigonometric
functions.
Unit II: Algebra
3. Matrices
Concept, notation, order, equality, types of matrices, zero and identity
matrix, transpose of a matrix, symmetric and skew symmetric matrices.
Operation on matrices: Addition and multiplication and multiplication
with a scalar. Simple properties of addition, multiplication and scalar
multiplication. Noncommutativity of multiplication of matrices and
existence of non-zero matrices whose product is the zero matrix
(restrict to square matrices of order 2). Concept of elementary row and
column operations. Invertible matrices and proof of the uniqueness of
inverse, if it exists; (Here all matrices will have real entries).
4. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of
determinants, minors, co-factors and applications of determinants in
finding the area of a triangle. Adjoint and inverse of a square matrix.
Consistency, inconsistency and number of solutions of system of linear
equations by examples, solving system of linear equations in two or
three variables (having unique solution) using inverse of a matrix.
Unit III: Calculus
5. Continuity and Differentiability
Continuity and differentiability, derivative of composite functions,
chain rule, derivatives of inverse trigonometric functions, derivative
of implicit functions. Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic
differentiation, derivative of functions expressed in parametric forms.
Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems
(without proof) and their geometric interpretation.
6. Applications of Derivatives
Applications of derivatives: rate of change of bodies,
increasing/decreasing functions, tangents and normals, use of
derivatives in approximation, maxima and minima (first derivative test
motivated geometrically and second derivative test given as a provable
tool). Simple problems (that illustrate basic principles and
understanding of the subject as well as real-life situations).
7. Integrals
Integration as inverse process of differentiation.Integration of a
variety of functions by substitution, by partial fractions and by parts,
Evaluation of simple integrals of the following types and problems
based on them.
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus
(without proof). Basic properties of definite integrals and evaluation
of definite integrals.
8. Applications of the Integrals
Applications in finding the area under simple curves, especially lines,
circles/parabolas/ellipses (in standard form only), Area between any of
the two above said curves (the region should be clearly identifiable).
9. Differential Equations
Definition, order and degree, general and particular solutions of a
differential equation.Formation of differential equation whose general
solution is given. Solution of differential equations by method of
separation of variables solutions of homogeneous differential equations
of first order and first degree. Solutions of linear differential
equation of the type:
dy/dx + py = q, where p and q are functions of x or constants.
dx/dy + px = q, where p and q are functions of y or constants.
Unit IV: Vectors and Three-Dimensional Geometry
10. Vectors
Vectors and scalars, magnitude and direction of a vector.Direction
cosines and direction ratios of a vector. Types of vectors (equal, unit,
zero, parallel and collinear vectors), position vector of a point,
negative of a vector, components of a vector, addition of vectors,
multiplication of a vector by a scalar, position vector of a point
dividing a line segment in a given ratio. Definition, Geometrical
Interpretation, properties and application of scalar (dot) product of
vectors, vector (cross) product of vectors, scalar triple product of
vectors.
11. Three – dimensional Geometry
Direction cosines and direction ratios of a line joining two
points.Cartesian equation and vector equation of a line, coplanar and
skew lines, shortest distance between two lines.Cartesian and vector
equation of a plane. Angle between (i) two lines, (ii) two planes, (iii)
a line and a plane. Distance of a point from a plane.
Unit V: Linear Programming
12. Linear Programming
Introduction, related terminology such as constraints, objective
function, optimization, different types of linear programming (L.P.)
problems, mathematical formulation of L.P. problems, graphical method of
solution for problems in two variables, feasible and infeasible regions
(bounded and unbounded), feasible and infeasible solutions, optimal
feasible solutions (up to three non-trivial constraints).
Unit VI: Probability
13. Probability
Conditional probability, multiplication theorem on probability.
independent events, total probability, Baye’s theorem, Random variable
and its probability distribution, mean and variance of random variable.
Repeated independent (Bernoulli) trials and Binomial distribution.
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